Related papers: On Generalised Inflations of Right Modular Groupoi…
We find a general model of {\em single-field} inflation within the context of type IIB string theory compactified on large volume Calabi-Yau orientifolds with $h^{2,1} > h^{1,1} = 2$. The inflaton is the axion part of the complexified…
We study a generalized version of hilltop inflation where the standard hilltop potential has been raised to a power and we allow fractional numbers for both the original hilltop power ($m$) and the overall exponent ($n$). In the parameter…
Graph products of monoids provide a common framework for direct and free products, and graph monoids (also known as free partially commutative monoids). If the monoids in question are groups, then any graph product is, of course, a group.…
Despite its central role in modern cosmology, doubts are often expressed as to whether cosmological inflation is really a falsifiable theory. We distinguish two facets of inflation, one as a theory of initial conditions for the hot big bang…
Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
Let $R$ be a commutative unital ring, $a\in R$ and $t$ a positive integer. $a^{t}$-reduced $R$-modules and universally $a^{t}$-reduced $R$-modules are defined and their properties given. Known (resp. new) results about reduced $R$-modules…
A groupoid that satisfies the left invertive law: $ab\cdot c=cb\cdot a$ is called an AG-groupoid. We extend the concept of left abelian distributive groupoid (LAD) and right abelian distributive groupoid (RAD) to introduce new subclasses of…
We propose a new class of inflation model, G-inflation, which has a Galileon-like nonlinear derivative interaction of the form $G(\phi, (\nabla\phi)^2)\Box\phi$ in the Lagrangian with the resultant equations of motion being of second order.…
Higgs G-inflation is a Higgs inflation model with a generalized Galileon term added to the standard model Higgs field, which realizes inflation compatible with observations. Recently, it was claimed that the generalized Galileon term…
Let $G$ be a locally compact group. We prove that the augmentation ideal in $L^1(G)$ is (algebraically) finitely-generated as a left ideal if and only if $G$ is finite. We then investigate weighted versions of this result, as well as a…
We introduce the framework of modular inflation with level structure, generalizing the level one theory considered previously to higher levels. We analyze the modular structure of CMB observables in this framework and show that the…
We present a concrete realization of tribrid inflation within the framework of the gauge group $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$. In this model, inflation is driven by the neutral components of left-handed Higgs…
If $S$ is a discrete semigroup, then $\beta S$ has a natural, left-topological semigroup structure extending $S$. Under some very mild conditions, $U(S)$, the set of uniform ultrafilters on $S$, is a two-sided ideal of $\beta S$, and…
We extend the lifting methods of our previous paper to lift reducible odd representations $\bar{\rho}:\mathrm{Gal}(\overline{F}/F) \to G(k)$ of Galois groups of global fields $F$ valued in Chevalley groups $G(k)$. Lifting results, when…
Using only general properties of the tachyon potential we show that inflation may be generic when many branes and anti-branes become coincident. Inflation may occur because of: (1) the assistance of the many diagonal tachyon fields; (2)…
Reasonable-looking models of inflation are compared, taking into account the possibility that the curvature perturbation might originate from some "curvaton" field different from the inflaton.
We propose a novel modified gravity: unimodular generalization of the Born-Infeld-$f(R)$ gravity within the framework of cosmology. After formulating the action corresponding to the generalized Born-Infeld-$f(R)$ gravity, we present a…
For a Banach left module action, we will extend some propositions from Lau and $\ddot{U}$lger and others into general situations and we establish the relationships between topological centers of the left module action with the multiplier…
The leading order dynamics of the type IIB Large Volume Scenario is characterised by the interplay between $\alpha'$ and non-perturbative effects which fix the overall volume and all local blow-up modes leaving (in general) several flat…